Prince Harry and the Walking with the Wounded expedition, including two Australians, are expected to reach the South Pole on Friday the 13th - which he says is "unlucky for some, lucky for us".
The adventurers, including wounded Australian soldiers Heath Jamieson and Seamus Donaghue, are nearing the end of their gruelling 321.8km trek across Antarctica and have their goal almost in sight.
Harry, who is patron of the expedition, said on Thursday: "A half day and we get to the South Pole on Friday 13th. Unlucky for some, lucky for us.
"The wind has dropped down, which is nice. I think everyone is feeling a bit tired but slowly getting into the rhythm. Only just got into the rhythm now and it has almost finished."
The 29-year-old prince has already said spirits are high following the decision to suspend the competitive element of the trek.
Harry has been part of a British group racing to the South Pole against teams from the Commonwealth and the US.
The competition was stopped over the weekend after some of the adventurers, who include injured servicemen and women, became very tired after encountering difficult terrain.
"Everyone is beginning to get quite excited, we can see the end in sight now,: said Ed Parker, the expedition's director and co-founder of the Walking with the Wounded charity.
"Everyone is thinking quite a lot about the journey that's behind us and it is not just the last three weeks up here in Antarctica but the year it has taken us to get here.
"A lot of people have overcome many injuries and issues to be here. It feels very special that this group of people is finally on the cusp of achieving our aim."
In a voice blog recorded in the frozen waste and released on Wednesday, the prince said: "Everyone is in really high spirits. The race obviously got cancelled a couple of days ago - a really good thing that has happened."
Looking ahead to reaching their goal, Harry highlighted fellow adventurer Duncan Slater, who lost both his legs when an improvised explosive device blew up in his vehicle in Afghanistan in 2009.
"Everyone just can't wait to get to the end. I think mixed emotions probably. I think some people, for instance Duncan, double amputee, simply doesn't find walking to the South Pole a big enough challenge, which is why he really enjoyed the race," the prince said.
"I think everyone back home will appreciate the fact that just being able to walk 100km in these conditions with no legs is a pretty amazing feat in itself."
In total, 12 injured service personnel who have overcome life-changing injuries are taking part in the expedition.
